235 
Sec. 11 -2)- Eq. 82 
for the ideal case (see Eq. (46)). Equating these expressions, one obtains 
Tt C4 ~(npR/2 Boi) 
Ta; O,#nR OL (F-1) - (n,RF 5" /2y,, ue) (82) 
Strictly speaking the value of C, in the denominator should be evaluated 
at Toy and that in the numerator at To, put these values differ so little 
that the value at To;can be used for both. 
e. Tables of D/Dy. The above results have been incorporated in 
Bq. (68) for D/D; and tables computed of D/D, vs x1, (x, is proportional to 
the density of loading) for three values of C;/no. The results are suf- 
ficiently insensitive to C;/np so that these three tables are sufficient, 
These tables also give Hy Le They are included in the appendix, as 
calculated by Dr. D. P. MacDougall and Dr. L. Epstein, In order to compute 
D for a given explosive, the procedure is therefore to calculate D; first, 
then to get D/D; for the given density of loading from the appropriate 
table. In ordér to do this, however, it is necessary to know the value of 
K, the "covolume constant", which enters the equation of state. The evalua- 
tion of K will be discussed in the next section, 
ll. _ Determination of Covolumes and Comparison with Experiment. 
a. Method of evaluating K. It is difficult to obtain sufficiently 
accurate values of the "covolume constant" K from direct experiments on 
gases because the equation of state used does not apply very well at easily 
attainable temperatures, where attractive forces play an important part. 
From a practical viewpoint, it is better to use the available data on 
experimental detonation velocities and work backwards to obtain a rule for 
evaluating the constant K. This rule can then be used to compute K and then 
D for a new substance. 
b. Effect of density of loading. As a first test of the theory, the 
values of K which bring the calculated and observed values of D into agree- 
ment, were computed for a large number of different densities of loading of 
PETN by Dr. MacDougall and Dr. L. Epstein of the Bureau of Mines. The ex- 
perimental measurements of three observers were included. If the basic 
theory, the form of the equation of state, the various approximations made, 
‘ and the experimental measurements were all satisfactory, the K's so obtained 
should be the same. Table 11-1 shows how nearly this ideal result is 
achieved.* The worst deviation of any value of K from the average is iis 
and the great majority of the deviations are less than 3%, The experimental 
error is at least that Great, as judged by the disagreements between the dif- 
ferent investigators. Similar constancy of K is found in other cases also. 
This gives us considerable confidence in the method. 
c. Different explosives. Next K was calculated for a number of dif- 
ferent explosives. Its value should depend on the composition of the burnt 
Ty 
* Actually K/to" is plotted but 71 varies only slightly over the range 
of densities used. 
